Robust classical and quantum communication over almost-iid channels

Abstract

The independent and identically distributed (iid) paradigm for asymptotic communication through quantum channels describes $n$ uses of a channel $Φ$ by $Φ^{\otimes n}$. Since exact tensor-power behaviour is an idealization, we ask whether the asymptotic capacities of $Φ$ remain achievable for channel sequences that are almost-iid along $Φ$. We consider sequences of Choi-almost-iid channels whose normalized Choi states are Mazzola-Sutter-Renner (MSR) almost-iid along the normalized Choi state of $Φ$, with defect parameters $r_n=o(n)$. In Renner's exponential de Finetti theorem for quantum states, almost-iid states appear in the approximating mixture and motivate the MSR almost-iid class. Choi-almost-iid channels play the corresponding role in an exponential de Finetti theorem for quantum channels established in a companion paper. In this paper, we prove that the universal unassisted classical and quantum capacities of the class of Choi-almost-iid channels along $Φ$ equal those of the channel $Φ$. Here universality is within this class: for each rate below the relevant capacity, a code sequence depending on $Φ$ and the rate, but not on the particular channel sequence, achieves vanishing error for every sequence in the class.